Six sigma workbook for dummies by craig gygi and bruce williams

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®

Six Sigma
k
o
o
b
k
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FOR

S
E
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M
U
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by Craig Gygi
Bruce Williams
Terry Gustafson


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®

Six Sigma
Workbook
FOR

DUMmIES

‰


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®

Six Sigma
k
o
o
b
k
r
o

W
FOR

S
E
I
m
M
U
D

‰

by Craig Gygi
Bruce Williams
Terry Gustafson


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Six Sigma® Workbook For Dummies®
Published by
Wiley Publishing, Inc.
111 River St.

Hoboken, NJ 07030-5774
www.wiley.com

Copyright © 2006 by Wiley Publishing, Inc., Indianapolis, Indiana
Published by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
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About the Authors
Craig Kent Gygi began studying and applying the elements of Six Sigma well before they
were formalized into today’s renowned breakthrough method. As an engineering graduate
student at Brigham Young University in the early 1990s, he integrated these then-unorganized
improvement techniques into his research and coaching of student product development
teams. Upon beginning his career in 1994 at Motorola’s Advanced Manufacturing Research
Lab in Florida, he was formally introduced to the just-formalizing Six Sigma method. It resonated deeply with his previous findings. From that time, Craig has applied, taught, and led
Six Sigma in all his endeavors, including management and technical capacities at Motorola,
Iomega, and General Atomics.
In 1998, Craig founded TolStack, Inc., to develop commercial Six Sigma software tools. He also
worked for several years as a technical colleague of Dr. Mikel J. Harry, the original consultant

of Six Sigma, co-developing and teaching new advances in its theory and application. In 2002,
Craig co-founded Savvi International, into which TolStack merged. Savvi provides solutions
for business performance improvement using Six Sigma, Lean, and Business Process
Management techniques. Craig acted as the director of Savvi’s products, service, and tools.
Today, Craig works with companies in the USA and internationally to integrate Six Sigma
practices directly into their core operations.
A Master Black Belt, Craig has wielded Six Sigma techniques now for over 13 years, spanning
projects from design to manufacturing to business management. He is also an expert teacher,
having instructed and mentored at all levels of Six Sigma, from executives to White Belts.
Bruce David Williams has been fascinated with complex systems since the launch of Sputnik
on his third birthday. With undergraduate degrees from the University of Colorado in Physics
and Astrophysics, he entered a career in aerospace systems, where he first encountered
Six Sigma after Motorola won the inaugural Baldridge Award in 1988. Later, with graduate
degrees in technical management and computer science from Johns Hopkins University and
Colorado, and as a member of the Hubble Telescope development team, he was intrigued
by how breakdowns in the smallest components could lead to colossal system failures. He
entered the Six Sigma industry for good in the mid-1990s when he founded a software company to pursue product life-cycle traceability.
Bruce has since been founder and CEO of two Six Sigma research and technology firms, and is
now Chairman and CEO of Savvi International, a provider of solutions for business performance improvement using Six Sigma, Lean, and Business Process Management techniques. He
resides in the highly-variable environment of the desert foothills of North Scottsdale, Arizona,
with his wife, two children, and a normal distribution of dogs, cats, birds, and horses.
Terry James Gustafson comes out of the world of business and finance, and brings a practical and entrepreneurial perspective to Six Sigma. After an undergraduate degree in finance
from Baldwin-Wallace, and an MBA degree from Kent State, he began his career in the field of
accounting with KPMG Peat Marwick in 1969, and advanced to a Partner position in auditing.
After leaving public accounting in 1990, Terry helped found, build, and operate a series of
technology-based entrepreneurial ventures, including venture-backed companies as well as
a public company.
In 2002, Terry co-founded Savvi International, which provides solutions for business performance improvement using Six Sigma, Lean, and Business Process Management techniques.
Terry serves as Savvi’s chief finance and operations officer.
Since founding Savvi, Terry has been immersed in Six Sigma techniques, helping to design

and develop Savvi’s training courses in Six Sigma and Lean. In addition, he has extensively
taught Six Sigma courses, both in a classroom and as an online instructor.


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Dedication
Craig Gygi: To Darren, a true brother.
Bruce Williams: To my mom and dad, Jane and Coe. When it comes to cause and effect, they
wrote my book!
Terry Gustafson: To my incredible wife, Sherrie, for putting up with all my entrepreneurial
nonsense without once using the term “dummy.”

Publisher’s Acknowledgments
We’re proud of this book; please send us your comments through our Dummies online registration form located at
www.dummies.com/register/.
Some of the people who helped bring this book to market include the following:
Acquisitions, Editorial, and Media Development

Composition

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Publishing and Editorial for Consumer Dummies
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Publishing for Technology Dummies
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Composition Services
Gerry Fahey, Vice President of Production Services
Debbie Stailey, Director of Composition Services

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Contents at a Glance
Introduction.................................................................................1
Part I: Getting Started in Six Sigma...............................................5
Chapter 1: Getting Ready for Six Sigma: The Effects of Variation ..........................................................7
Chapter 2: Forming a Six Sigma Initiative................................................................................................13
Chapter 3: Leading and Managing a Six Sigma Initiative .......................................................................27

Part II: Defining a Six Sigma Project ...........................................43
Chapter 4: Putting the Right Foot Forward: Defining a Six Sigma Project...........................................45
Chapter 5: Brainstorming the Inputs to Your Process...........................................................................53
Chapter 6: Prioritizing Which Inputs to Address ...................................................................................69

Part III: Mastering Measuring .....................................................85
Chapter 7: Categorizing Data and Calculating Measures of Variation .................................................87
Chapter 8: A Picture’s Worth 1,000 Words: Measuring with Charts and Graphs .............................107
Chapter 9: Yield and Defects: Calculating the Good, the Bad, and the Ugly ....................................129

Part IV: Assessing the Right Approach to Your Analysis ..............141
Chapter 10: Mastering Measurement System Analysis (MSA) ...........................................................143
Chapter 11: Capability: Matching Performance to Need.....................................................................155

Chapter 12: Narrowing Your Inputs with Confidence ..........................................................................169

Part V: Improving and Controlling .............................................183
Chapter 13: Quantifying Variable Relationships...................................................................................185
Chapter 14: Planning and Conducting 2k Factorial Experiments .......................................................209
Chapter 15: Constructing Control Plans and Charts ...........................................................................239

Part VI: The Part of Tens...........................................................281
Chapter 16: Ten Implementation Myths of Six Sigma ..........................................................................283
Chapter 17: Ten Tips for Finishing a Six Sigma Project Successfully.................................................287

Index.......................................................................................291


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Table of Contents
Introduction .................................................................................1
About This Book.........................................................................................................................1
Conventions Used in This Book ...............................................................................................2
What You’re Not to Read...........................................................................................................2
Foolish Assumptions .................................................................................................................2
How This Book Is Organized.....................................................................................................2
Part I: Getting Started in Six Sigma ................................................................................2
Part II: Defining a Six Sigma Project ...............................................................................3
Part III: Mastering Measuring..........................................................................................3
Part IV: Assessing the Right Approach to Your Analysis ............................................3
Part V: Improving and Controlling .................................................................................3
Part VI: The Part of Tens .................................................................................................4
Icons Used in This Book............................................................................................................4
Where to Go from Here..............................................................................................................4

Part I: Getting Started in Six Sigma ...............................................5
Chapter 1: Getting Ready for Six Sigma: The Effects of Variation .................................7
Recognizing Variation around You...........................................................................................7
Evaluating Variation and Business Performance with Y = f(X) + f .......................................9
Breaking down Y = f(X) + f to a simple process............................................................9
Applying Y = f(X) + f: A practice example .....................................................................9
Assessing the Impact of Variation on Business Performance ............................................11

Chapter 2: Forming a Six Sigma Initiative........................................................................13
Planning Your Key Business Objectives (KBOs) ..................................................................13
Establishing a KBO checklist ........................................................................................14
Verifying your process alignment.................................................................................15
Determining the Proper Training Program ...........................................................................16

Who will manage the training program? .....................................................................16
Finding the expertise within your organization .........................................................16
Scoping the training program .......................................................................................17
Recognizing cultural predisposition ............................................................................19
Defining the training plan..............................................................................................20
Deciding Who Will Conduct the Training..............................................................................21
Teaming for Success: Shopping for Your Implementation Partners..................................24
Pricing and Contracting Approaches ....................................................................................26

Chapter 3: Leading and Managing a Six Sigma Initiative.............................................27
Selecting Your Leadership Team............................................................................................27
Approaching the selection process .............................................................................27
Go, team: Unifying individuals to create a team.........................................................30
Implementing Your Communications Plan ...........................................................................31
Understanding the two communications plans .........................................................31
Elements of your communications plan......................................................................31
What’s to communicate? ...............................................................................................32
Who does the communicating? ....................................................................................33
Timing is everything ......................................................................................................36


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Using communications tools ........................................................................................36
Where, oh, where have the communications gone? ..................................................36
Writing your communications plans............................................................................38
Selecting Software Products and Integrating Information Technology Architectures .......39
Yours, mine, or ours: Platform questions ...................................................................39
Practitioner tools ...........................................................................................................40
Management tools ..........................................................................................................40
Enterprise Integration, SOA, and BPM.........................................................................41
Defining and Implementing Your Management Plan............................................................41

Part II: Defining a Six Sigma Project ............................................43
Chapter 4: Putting the Right Foot Forward: Defining a Six Sigma Project.................45
Getting Project Ideas by Using the Business Case Writing Tool ........................................45
Prioritizing and Aligning Projects with Business-Customer-Process Scorecards............46
Project Definition I: Writing a Problem Statement ...............................................................48
Project Definition II: Writing an Objective Statement..........................................................49
Launching a Project .................................................................................................................51
Solutions to Defining a Six Sigma Project..............................................................................52

Chapter 5: Brainstorming the Inputs to Your Process....................................................53
All Together Now: Brainstorming with Your Team to Create Affinity Diagrams ..............53
Dem Bones: Creating Fishbone Diagrams .............................................................................57
Examining Your Processes with Process Flow Maps...........................................................60
Finding Critical Fruit in the CT Tree ......................................................................................62
Solutions to Brainstorming the Inputs Problems ................................................................65

Chapter 6: Prioritizing Which Inputs to Address ............................................................69
Weeding and Pruning the Input Garden: Using Pareto Diagrams ......................................69

Cementing the Foundation: Creating SIPOC Diagrams........................................................71
Untangling Webs: Creating a Cause-and-Effect Matrix ........................................................73
Performing a Failure Modes Effects Analysis (FMEA) .........................................................76
Solutions to Prioritizing Inputs Problems.............................................................................80

Part III: Mastering Measuring......................................................85
Chapter 7: Categorizing Data and Calculating Measures of Variation.......................87
Differentiating Data Types ......................................................................................................87
Calculating Measures of Variation Location .........................................................................89
Variety Is the Spice of Life: Measuring Variation Spread.....................................................92
Time Warp: Separating Short-Term and Long-Term Variation............................................94
Solutions to Categorizing Data and Calculating Measures of Variation Problems ........100

Chapter 8: A Picture’s Worth 1,000 Words: Measuring with Charts and Graphs ....107
Putting Dot Plots or Histograms to Use ..............................................................................107
Setting Up Box and Whisker Plots .......................................................................................110
Seeing Spots: Using Scatter Plots.........................................................................................114
Hindsight Is 20/20: Using Process Behavior or Time Series Charts ................................119
Solutions to Exercises for Yields and Defects Problems...................................................121


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Table of Contents

Chapter 9: Yield and Defects: Calculating the Good, the Bad, and the Ugly ...........129
Get Real: Creating Realistic Specifications .........................................................................129
Getting It Right the First Time: Calculating First Time Yield (FTY).................................131
Rolling Many into One: Calculating Rolled Throughput Yield (RTY) ..............................132
“How Bad Is It, Doc?” Calculating Defect Rates..................................................................134
What’s Missing? Linking Yield to Defects............................................................................136
Solutions to Yield and Defects Problems............................................................................138

Part IV: Assessing the Right Approach to Your Analysis...............141
Chapter 10: Mastering Measurement System Analysis (MSA)..................................143
Your Basic Sanity Check: Auditing Measurement Systems...............................................143
Do We Agree? Performing an Attribute Measurement System Analysis ........................146
Gauging Gages: Analyzing Continuous Variable Measurement Systems ........................150
Solutions to MSA Problems ..................................................................................................153

Chapter 11: Capability: Matching Performance to Need.............................................155
Calculating and Interpreting Sigma (Z) Scores...................................................................155
Shift Happens: Transforming Between Short- and Long-Term Performance..................158
Calculating and Interpreting Capability Indices.................................................................160
Prescribing an Improvement Plan........................................................................................160
Solutions to Capability Problems.........................................................................................165

Chapter 12: Narrowing Your Inputs with Confidence ..................................................169
Creating Confidence Intervals for Means............................................................................170
Calculating Confidence Intervals for Standard Deviations...............................................173
Four Out of Five Recommend: Using Confidence Intervals for Proportions ..................176
Solutions to Narrowing Inputs Problems ............................................................................179

Part V: Improving and Controlling ..............................................183
Chapter 13: Quantifying Variable Relationships ...........................................................185

Quantifying Correlation between Variables........................................................................185
Fitting Lines to Variable Relationships................................................................................190
Assessing the Adequacy of a Fitted Line ............................................................................192
Solutions to Quantifying Variable Relationships Problems ..............................................197

Chapter 14: Planning and Conducting 2k Factorial Experiments ...............................209
Don’t Be a Frankenstein: Planning Experiments ................................................................209
Managing Those Pesky Nuisance Variables........................................................................212
Calculating Main Effects ........................................................................................................214
Calculating Interaction Effects .............................................................................................219
Determining Which Effects Are Significant .........................................................................224
The Ultimate Power Trip: Forming Y = f(X) Equations......................................................227
Solutions to 2k Factorial Experiment Problems..................................................................229

Chapter 15: Constructing Control Plans and Charts .....................................................239
Doing the Poka-Yoke: Mistake-Proofing Products or Processes ......................................239
Forming Control Plans to Maintain Your Improvements ..................................................241
Selecting the Right Control Chart for Your Situation ........................................................242
Interpreting Your Control Charts .........................................................................................245

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Constructing an Individuals and Moving Range (I-MR) Chart..........................................249
Raising the Bar for Small Samples: Averages and Ranges ( X-R) Charts.........................252
Making a p Chart for Your Attribute Data ...........................................................................256
Creating a u Chart for Your Attribute Data .........................................................................260
Solutions to Control Plan and Chart Problems ..................................................................265

Part VI: The Part of Tens ...........................................................281
Chapter 16: Ten Implementation Myths of Six Sigma ..................................................283
Six Sigma Is about Achieving “Six Sigma” ...........................................................................283
Six Sigma Will Make Us Start All Over Again with Something Different ..........................284
Six Sigma Stifles Creativity....................................................................................................284
Modeling Processes Is Too Complicated and Doesn’t Go Anywhere ..............................284
Six Sigma Is Another “Program of the Month” ...................................................................285
Six Sigma Is Just a Quick-hit, Cost-Reduction Initiative ....................................................285
Six Sigma Is Too Onerous and Prescriptive ........................................................................285
You Can’t Implement Six Sigma Yourself.............................................................................285
The Six Sigma Approach Is Way Too Expensive and Disruptive ......................................286
If You’re Not Doing Black Belt Projects, You’re Not Really Doing Six Sigma ..................286

Chapter 17: Ten Tips for Finishing a Six Sigma Project Successfully ......................287
Properly Scoping Your Project .............................................................................................287
Anticipating Scope Creepy-Crawlies....................................................................................287
Charting the Entire Course ...................................................................................................288
Making Sure the Right People Are Aboard..........................................................................288
Remembering That Short Is Sweet.......................................................................................288
Setting Achievable Goals.......................................................................................................289

Communicating for Success .................................................................................................289
Satisfying the Stakeholders...................................................................................................289
Maintaining Active and Unwavering Support.....................................................................289
Applying Formal Project Management ................................................................................290

Index .......................................................................................291


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Introduction

S

ix Sigma is the single most effective problem-solving methodology for improving business and organizational performance. There’s not a business, technical, or process
challenge that can’t be improved with Six Sigma. The world’s top corporations have used it
to increase their profits collectively by more than $100 billion over the past ten years. In
certain corporations, Six Sigma proficiency on your resume is now a prerequisite to moving
into a management position.
If you’re part of a Fortune 500 company — particularly a manufacturing company — chances
are you’ve heard about Six Sigma. You may even have been through a training regimen and
been part of a corporate initiative or an improvement project. If so, you know the capabilities
of Six Sigma; you have witnessed its power and achievements firsthand.
But if, like most people, you’re outside of the upper echelons of big business, Six Sigma isn’t

well known. It has been too expensive and complicated for small- and medium-sized businesses, public institutions, not-for-profit organizations, educational environments, and aspiring individuals. Its potential has remained out of reach for the vast majority of professionals
and organizations world-wide.
Fortunately, all this is changing. As the methods and tools of Six Sigma have spread, it has
become easier to understand, less expensive to learn, and more straightforward to implement. The mysteries of Six Sigma have been revealed.
Simply stated, Six Sigma is about applying a structured, scientific method to improve any
aspect of a business, organization, process, or person. It’s about engaging in disciplined data
collection and analysis to determine the best possible ways of meeting your customers’
needs while satisfying your own, and by minimizing wasted resources and maximizing profit
in the process.

About This Book
This workbook is unique. What used to only be available through expensive consultant-led
professional training is laid out in simplicity here. This workbook includes step-by-step explanations and examples of the tools, methods, formulas, and tactics of Six Sigma. Exercises and
practice problems build your mastery in applying the tools and techniques. And ready-to-use
templates and worksheets provide you immediate access to the power of Six Sigma.
Corporate Six Sigma training also uses expensive calculation software like Minitab. Using
expensive calculation software is fine if your company can provide you with $1,000 software
programs, but everyone else is priced out. Not to worry! In this workbook, we’ve provided
all the formulas and calculations, so that with simple explanations, you can perform these
same calculations quickly by hand. The only price is the cost of this workbook (and a box of
Number 2 pencils!). Or you can automate them using your favorite spreadsheet software.
Together with the more conceptual Six Sigma For Dummies, Six Sigma Workbook For Dummies
truly forms a 2-volume box set for “Six Sigma in a box.” Just add a little practice, and you’re
ready to join the growing ranks of professionals who list Six Sigma as a critical competency to
their success. And be sure to keep a notebook handy for working out problems, as some of
them will require a bit more “scrap paper” than even a workbook can provide.


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Conventions Used in This Book
Mathematical formulas and variables used in this workbook are written in an italicized
font. This will help you pick them out from the rest of the text and explanations.

What You’re Not to Read
Even after all the hard work we’ve put into this workbook, we don’t expect you to read
every word of it! Its purpose is application, so read only what you need to gain mastery of the skill or topic. You don’t have to do every practice problem. We’ve included
several problems on each concept just in case you need the practice.

Foolish Assumptions
Six Sigma has a lot of math and statistics in it. We assume you’re familiar with basic
arithmetic operations — adding, subtracting, multiplying, and dividing. At some points
it does get a little more complicated than that, but not much and not very often.
We also assume that you have a context in which to apply the tools and techniques of
Six Sigma. It may be a bona fide Six Sigma project you have been assigned to and are
working on. Or it may be an improvement effort of your own creation. Or it may even be
an aspect of your personal life you want to improve. In any case, as you read through
this workbook, try out the tools you’re discovering. It’s the quickest path to proficiency.

How This Book Is Organized

This workbook is organized along the lines of DMAIC — that’s Define, Measure, Analyze,
Improve, and Control — the problem-solving methodology of all Six Sigma thinking and
working. If you need help with a specific task, you can jump into the workbook at that
specific point along the DMAIC roadmap to get the focused practice or guidance you
need. Or, if you want to gain a comprehensive mastery of all the skills of Six Sigma, you
can follow through from the first page to the last.

Part I: Getting Started in Six Sigma
In Part I, you find guidance, checklists, and templates for organizing your launch into
Six Sigma. This part could be for yourself or it could be for getting an entire organization ready to head down the Six Sigma path. From aligning with key business objectives to forming a management communications plan, there’s a lot of preparation when
starting a breakthrough improvement journey.
Chapter 1 provides a first-hand, live introduction to the issues of variation and
improvement. Chapter 2 gives you tools and worksheets for forming and aligning the
improvement work with your organization’s key business objectives. Chapter 3 provides checklists, templates, and examples for setting up an organization-wide Six
Sigma program.


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Introduction

Part II: Defining a Six Sigma Project
Part II is all about defining the improvement work you do in Six Sigma. If you’re starting a Six Sigma project, this is the part for you. You practice generating viable project
ideas, find templates for scoping your work, and complete exercises for setting breakthrough objectives and goals.

Chapter 4 contains examples and templates for correctly defining each Six Sigma project. Chapter 5 gives you expertise in all the tools for identifying the potential causes of
poor performance. Going through Chapter 6, you discover how to whittle down a host
of potential causes to a handful of the “critical few.”

Part III: Mastering Measuring
Part III is full of exercises and practice for mastering the skills of measuring. If you don’t
measure it, you can’t know it. If you don’t know it, you can’t control it. If you can’t control it, you’re at the mercy of chance. And nobody wants to be in that position!
In Chapter 7, you find exercises for discovering how to collect data and calculate its
statistical characteristics. Chapter 8 is a guide to the powerful skills of creating and
interpreting charts, graphs, and plots. The practice problems in Chapter 9 show you
how to measure the capability of your system or process.

Part IV: Assessing the Right
Approach to Your Analysis
Understanding what your measurements mean is the focus of Part IV. In this part, you
find exercises that show you how to perform critical analyses of your collected measurements, uncover root causes, and confirm hypotheses.
In Chapter 10, you find calculation templates for analyzing your measurement system.
Chapter 11 covers the topic of capability — you find out how to calculate whether
your process meets its performance requirements. Throughout Chapter 12 you practice calculating confidence intervals to statistically analyze differences among inputs
and outputs.

Part V: Improving and Controlling
The final stages of DMAIC are Improve and Control. Skills for synthesizing improvements to solve problems can be mastered by anyone through the exercises and worksheets provided in this part. And you can’t neglect Control — be sure to become
proficient in the skills of controlling and maintaining the improvements you make.
Chapter 13 gives you the skills to quantify how one factor affects another. This is done
through correlation and curve fitting. Chapter 14 shows you all the aspects of designing, conducting, and analyzing 2k factorial experiments. In Chapter 15, you practice creating Poka-Yokes, control plans, and statistical process control charts.

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Six Sigma Workbook For Dummies

Part VI: The Part of Tens
In this part, we provide you with two helpful top ten lists. Chapter 16 debunks the
ten most common myths about Six Sigma and Chapter 17 lists the ten most critical
things to do to complete a Six Sigma project. And be sure to check out www.dummies.
com/go/sixsigmaworkbook for bonus forms that you can print for your own use.

Icons Used in This Book
Throughout the workbook, you’ll see symbols in the margins called icons. These icons
highlight special types of information. When you see any of the following icons, this is
what they mean:
Each section of this workbook begins with a brief overview of the topic. After the intro,
you see an example problem with a fully worked solution for use as a reference when
you work the practice problems. You can quickly locate the example problems by looking for this icon.

These are handy points that help you perform and apply some of the trickier parts of
Six Sigma more quickly and correctly.

This icon is used in almost every section of the workbook. It lets you know that the

associated text summarizes the key application principles, formulas, or procedures
needed for that particular skill.

When you see this icon, it alerts you to be aware of a particular risk or pitfall that
could cause you trouble.

Where to Go from Here
The beauty of a For Dummies book is that you don’t have to start at the beginning and
work your way through every page. Instead, each chapter is self-contained; you can
start with whichever chapter interests you the most and then jump to wherever you
want to go next.
Here are some suggestions on where to start:
ߜ If you already have a Six Sigma project picked out or assigned to you, start in
Chapter 4. You’ll find practice there on properly defining your problem and its
intended solution.
ߜ If you have a specific Six Sigma task to perform and just need some practice on
it, start in the Table of Contents. Find the topic you need and go to it. In no time
your skills for that task will be honed and ready to go.
ߜ If you’re forming a Six Sigma initiative for your organization, start in Chapters 2
and 3.


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Part I

Getting Started in Six Sigma


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S

Page 6

In this part . . .

ix Sigma starts with initiative — either your own or
your organization’s. This part provides you and your
colleagues with useful exercises and templates for recognizing, organizing, and launching your journey to breakthrough improvement.


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Chapter 1

Getting Ready for Six Sigma:
The Effects of Variation
In This Chapter
ᮣ Realizing that variation is everywhere
ᮣ Mastering the Six Sigma breakthrough equation
ᮣ Exploring the effect of variation on business performance

T

he characterization, measurement, analysis, and control of variation is the central theme
of Six Sigma. Every process and every product is affected by variation. Variation —
within limits — is okay, and is even desirable. However, you can actually have too much
variation. If undesirable variation is out of control, failure is the result!
The key goals of Six Sigma are to fix undesirable variation, ignore variation that doesn’t
matter, and allow for variation that can’t be fixed. Many of the tools and techniques in this
workbook help you determine whether your variation is desirable or undesirable. These
tools also show you how to fix the variation that can actually be fixed, so that your efforts
are concentrated where you can make the most improvement impact.

Before you go any further in this workbook, however, you must accept two undeniable truths
about variation: Every output varies and every input varies. Don’t you feel better now that
you’ve accepted the fact that variation happens? It’s simply a fact of life. You can now focus
on finding and correcting as much of that variation as possible — making your processes
and products the best they can be. Please also check out www.dummies.com/go/sixsigma
workbook for some useful forms you can print out.

Recognizing Variation around You
To get started recognizing the variation around you, use the variation journal in Figure 1-1

to chronicle the variation you encounter in a day of normal activities. Because you have
accepted that everything has variation, your daily journal could exceed the size of the
Library of Congress if you try to include everything that happens! Instead, try to concentrate on more significant events — events that, if impacted by unacceptable variation, could
have a negative effect on your life or job. Figure 1-2 is an example of the entries you might
make. Try to record at least 20 key items. As indicated on the worksheet, consider the type
of failure that the variation could cause, and whether the variation can be controlled.


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Part I: Getting Started in Six Sigma
Variation Journal
Date:

Activity

Undesirable Variation

Effect of Variation

Is Variation
Controllable?

Yes/No

Figure 1-1:
The Six
Sigma
variation
journal.

Variation Journal
Date:

Activity
Arriving at work
Figure 1-2:
Entry
examples
for the
variation
journal.

Undesirable Variation
Arriving late

Returning phone calls Calls returned late
Server slow to
Accessing server
respond or not
computer
available

Effect of Variation
Loss of wages, lost
business, lost job
Lost business,
irritation of boss

Inefficiency, lost data

Is Variation
Controllable?
Yes/No
Yes
Yes

Maybe


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Chapter 1: Getting Ready for Six Sigma: The Effects of Variation

Evaluating Variation and Business
Performance with Y = f(X) + f
The word “breakthrough” is bandied about all the time, particularly when advertising

some product — a breakthrough shaving system, breakthrough hair gel, a breakthrough mousetrap, and on and on. So, you have to be a bit cautious when claiming
something is a breakthrough product. But, Six Sigma practitioners don’t hesitate to call
the basic equation, Y = f(X) + f, a breakthrough equation. When you apply the concept
that all outcomes (Ys) are the result of some number of inputs (Xs) that interact in
some way — f, or the function — to produce that outcome, and that there are always
some other factors, either known or unknown — f, or epsilon — that will impact the
outcome, then you are well on your way to breakthrough improvements.
The elegance of the Y = f(X) + f equation is that it applies to anything and everything —
from the simplest process, such as mixing a drink, to the most complex, such as building a space shuttle. After a process is broken down into primary elements, you can
then identify the desired outcome, find the inputs that contribute to that outcome,
identify those inputs that really matter, recognize where error and variation might
occur, and plan improvements that will have a positive impact. This workbook gives
you guidance in applying these concepts and conducting improvement activities.

Breaking down Y = f(X) + f
to a simple process
Following is an example of a simple process with which almost everyone is familiar —
cooking eggs. If you apply Y = f(X) + f to this process, the results look like this:
ߜ Outcome (Y) — properly cooked eggs
ߜ Inputs (Xs) — eggs, oil, heat, pan, timer
ߜ Function (f) — shells are removed, oil is added to pan, eggs are placed in pan,
heat is applied for a specific time, eggs are removed
ߜ Epsilon (f) — size of eggs, age of eggs, temperature of eggs, thickness of pan,
amount of heat, timer accuracy, type of oil, altitude
Some of these factors can be quantified and controlled, but others can’t. The trick is to
determine which, if any, of these inputs have a significant impact on the outcome and
can be controlled. One of the basic tenets of Six Sigma is focusing efforts only on those
inputs that have a substantial impact and that are practical to address. Time and
resources would be wasted if you tried to improve the egg-cooking process by changing the altitude!

Applying Y = f(X) + f: A practice example
As practice, apply the Y = f(X) + f equation to a more complicated process, one much
like many business processes. Think about the equation as you read the story about a
house fire on Elm Street. Then use the worksheet in Figure 1-3 to match elements of
the story to the components of the equation. Here’s the story problem:

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Part I: Getting Started in Six Sigma
A house catches fire on Elm Street and a neighbor calls 911 to report the fire and
give the address. The 911 operator triggers an alarm in the nearest fire station and
transmits the address. When the alarm sounds, the firefighters dress, load the
truck, and leave the firehouse. Using a current map and an established route plan,
they find and take the most direct route to Elm Street. Halfway to Elm Street, they
encounter a major traffic jam, which is normal for that time of day, and have to
detour. Shortly thereafter, a freak sleet storm forces the truck to slow to a crawl.
When the truck finally arrives, the men hook up the hoses, but find that water
pressure is low and that water flow to the fire is significantly less than normal.
Eventually the flames are extinguished, but only after the house is a total loss.

Fortunately, all the residents of the house escaped without injury.
From the perspective of the fire department, identify a primary Y, at least ten important Xs, and the elements of error.

Y = f(X) + ε Worksheet
Output (Y)

Input (X)

Error

Figure 1-3:
The Y =
f(X) + f
exercise
worksheet.

Figure 1-4 is a solution to the practice house fire exercise. Even if your solution
includes different items, it’s okay. You have at least started thinking how the breakthrough equation applies to business processes.


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Chapter 1: Getting Ready for Six Sigma: The Effects of Variation
Y = f(X)+ ε Worksheet

Output (Y)
Put out the fire quickly

Figure 1-4:
The solution
to the
practice
house fire
exercise.

Input (X)

911 call
Fire station alarm
or: Prevent injuries or loss of life Address of fire
Map
Route plan
Training
Firefighter
Fire truck
Water
Hoses
Traffic

Error
Traffic
Sleet storm
Low water pressure

Assessing the Impact of Variation

on Business Performance
After you realize that variation is prevalent in all processes, you have to determine the
effect variation has on your process, and then you have to assess if it’s really a problem at all. After all, some variation is inevitable, and you can live with it, right? Well,
maybe, or maybe not.
Suppose you’re the general manager of Widgets International, the undisputed market
leader. You’re rightfully proud of your market position, and believe that producing the
highest quality widgets has lead you to where you are today. So, you’re taken aback
when an upstart Six Sigma Yellow Belt dares ask you about the true reliability of your
widget production process. “We produce the best darn widgets possible,” you retort.
“We just can’t do much to improve that process. Our rigorous assessments have determined that each and every step in the process is 95 percent reliable. Therefore, the
whole process is 95 percent reliable. How can we do better than that?”
The Yellow Belt persists, so you decide to humor her even though you’re confident
in your figures. “How many steps are there in the production process,” she asks.
Consulting your most recent production chart, you answer, “We have a total of 20 discrete steps.” The Yellow Belt then says, “Let’s do some calculations. If each of the first
two steps is 95 percent reliable, the chance of a widget making it through both steps
without a defect is 0.95 times 0.95, or 90.25 percent.” “Uhhh,” you respond eloquently,
“90 percent is still pretty good, right?” “Well, sure,” she says, “but we aren’t done yet.
The chance of a widget making it through the first three steps without a defect is 0.95
times 0.95 times 0.95, or 85.74 percent.” You begin to get a sinking feeling in the pit of
your stomach. Sweat begins to run down your face. You begin to see the big picture
and stammer, “Are you telling me that this calculation should be made through all 20
steps? What is the bottom line here?” She whips out her calculator and pounds in a
few numbers, and then she gives you the bad news: “Well, if each of the 20 steps is 95
percent reliable, the chance of a widget making it all the way through the process
without defect is 36 percent.”

11